Question

□PQRS and □MNRL are rectangles if point M is the midpoint of side PR then prove that LN =1/2SQ​

Answer 1

Given:

✰ □PQRS and □MNRL are rectangles.

✰ Point M is the midpoint of side PR.

To Prove:

✠ LN = 1/2 SQ

Proof:

Here in this question we will use midpoint theorem to prove the ab

We know that □PQRS and □MNRL are rectangles. All the four angles of a rectangle are equal.

So,

⤳∠RNM = ∠RQP = 90°

Point M is the midpoint of side PR.

Draw a line starting from point M straight to segment RQ, we will get point N.

⤳ MN || PQ

Draw a line starting from point M straight to segment SR, we will get point L.

⤳LR || PQ

∴ N and L are the mid-points of segment RQ and SR respectively. [ Converse mid-point theorem ]

By mid-point theorem,

LN || SQ

AND

LN = 1/2 SQ

HENCE PROVED!!

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